The following are two Energy2D simulations that compare convection and conduction, which should run within this page if you have installed Java and Java applets are enabled with your browser. The first one shows the case of natural convection. The second one shows the case of forced convection.
Instruction: Click inside a simulation window. Press 'R' to start or stop, 'T' to reset, 'L' to reload the initial configurations, and 'G' to open or close a graph. The virtual temperature sensors can be moved around, though most other pieces are locked to their positions. Rightclick on the windows for more actions.
Natural convection (driven by thermal buoyancy): 
Forced convection (driven by airflow): 
A Von Kármán vortex street.

More generally, Energy2D is a Java application that allows users to create interactive, realtime simulations of heat and mass flow. A simulation you create can be easily placed on the Internet just like what you saw above.
On a separate note, below are two results for conduction simulations using Energy2D that illustrate the circuit analogy: Ohm's Law is the electrical analogy of Fourier's Law of Heat Conduction. It is interesting to note that Ohm actually drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work (see Ohm's Law in Wikipedia). Ironically, today's students seem to be more familiar with Ohm's Law than Fourier's Law. So the circuit analogy is used in textbooks to help students understand heat conduction.
The analogy to a parallel circuit. 
The analogy to a series circuit. 